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人気のある微分積分 >

integral from 0 to 2 of (4t-1)^{10}

解

\int_{0}^{2} (4 t - 1)^{10} d t

解

\frac{7 ^{11} + 1}{44}

+1

十進法表記

44939244.18181 \dots

解答ステップ

\int_{0}^{2} (4 t - 1)^{10} d t

u置換積分法を適用する

= \int_{- 1}^{7} \frac{u ^{10}}{4} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{- 1}^{7} u^{10} d u

べき乗則を適用する

= \frac{1}{4} [\frac{u ^{11}}{11}]_{- 1}^{7}

限度を計算する:

\frac{7 ^{11}}{11} + \frac{1}{11}

= \frac{1}{4} (\frac{7 ^{11}}{11} + \frac{1}{11})

簡素化

= \frac{7 ^{11} + 1}{44}

グラフ

人気の例

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\int_{3}^{4} (x - 3) (4 - x) d x

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